I am not attorney and I have not been through a divorce or custody battle but I have consulted with an attorney. I do have similar experience however with a wife who drank and used Rx drugs for seven years, drove with the kids drunk, had a DUI, and went to rehab. She has been sober ever since rehab thankfully and coming up on 8 months.
The attorney I spoke to in PA said that her history would weigh heavily on a custody decision. Chances that a judge is going to grant full custody to someone who has proven to make poor life decisions that endanger people, especially children is pretty slim.
I don't know how this would compare in Utah, but I suspect it would be similar. I take it your wife is still drinking? If she is unable to demostrate a history of sobriety, it will certainly make her desire for custody more difficult to obtain.
I wish you well. Do what is best for you and your children.